--- Matthew Church said:

Quite a nice link for the SIR:

"In 1803, the Surrey Iron Railway was opened in Mitcham. It was the
first public railway to be sanctioned by Parliament and made Mitcham
the first place in the world to be served by a public railway. It used
horse drawn wagons to carry coal from the Thames at Wandsworth as far
as Croydon. On the way back from Croydon to Wandsworth, these wagons
carried flour, copper, paper and the town's most famous product -
Mitcham Lavender. The Georgian station at Mitcham is still in use, and
is one of the oldest railway stations in the world."

http://tinyurl.com/3rgo4

If this is the answer to the original posted question, I am not sure
it is correct. The building was built as a house and only adapted as a
station in the 1850's when the SIR was replaced by the 'conventional'
railway. There is no evidence that I know of to suggest it was
anything other than a private house when the SIR was built. The SIR
didn't have stations in the accepted sense as it served various
wharves and sidings etc for goods only. There was a loop and sidings
for a coal merchant here but it was on the south side of the line and
not where the station building is. The web site quoted is a bit
misleading here. Also, Mitcham was hardly the first place to be served
by a public railway. It was simply near the route of the line that
went to Croydon (much more important) and intended to go on to
Portsmouth.

Peter Heather